I have played both around 10 times...there are some superficial similarities, but they feel very different to me. I prefer Oh My Goods!, but you need to ensure that you are using the updated rules. Port Royal has a much stronger push your luck element while Oh My Goods! has some very satisfying production chains that can happen (easier in the new rules). Port Royal is definitely easier to teach and play (and still quite enjoyable), but I find Oh My Goods! to be a more fulfilling experience.
I would recommend Port Royale. It has quite a lot of luck involved and it's simple, but it's fun. Also, skip Oh My Goods, get Ora et Labora. ) Same illustrations, much deeper (and longer) game. The chains are as satisfying.